Path-Integral Calculation of the Mean Number of Overcrossings in an Entangled Polymer Network

1999 ◽  
Vol 39 (3) ◽  
pp. 550-557 ◽  
Author(s):  
Gustavo A. Arteca
Keyword(s):  
Path Integral ◽  
Polymer Network ◽  
Entangled Polymer ◽  
The Mean

PATH INTEGRAL APPROACH TO A SINGLE POLYMER CHAIN WITH RANDOM MEDIA

2004 ◽  
Vol 18 (10n11) ◽  
pp. 1465-1478 ◽  
Author(s):  
CH. KUNSOMBAT ◽  
V. SA-YAKANIT
Keyword(s):  
Polymer Chain ◽  
Path Integral ◽  
Random Media ◽  
Feynman Path Integral ◽  
Feynman Path ◽  
Short Range Correlation ◽  
Range Correlation ◽  
End Distance ◽  
Non Local ◽  
The Mean

In this paper we consider the problem of a polymer chain in random media with finite correlation. We show that the mean square end-to-end distance of a polymer chain can be obtained using the Feynman path integral developed by Feynman for treating the polaron problem and successfuly applied to the theory of heavily doped semiconductor. We show that for short-range correlation or the white Gaussian model we derive the results obtained by Edwards and Muthukumar using the replica method and for long-range correlation we obtain the result of Yohannes Shiferaw and Yadin Y. Goldschimidt. The main idea of this paper is to generalize the model proposed by Edwards and Muthukumar for short-range correlation to finite correlation. Instead of using a replica method, we employ the Feynman path integral by modeling the polymer Hamiltonian as a model of non-local quadratic trial Hamiltonian. This non-local trial Hamiltonian is essential as it will reflect the translation invariant of the original Hamiltonian. The calculation is proceeded by considering the differences between the polymer propagator and the trial propagator as the first cumulant approximation. The variational principle is used to find the optimal values of the variational parameters and the mean square end-to-end distance is obtained. Several asymptotic limits are considered and a comparison between this approaches and replica approach will be discussed.

scholarly journals Lefschetz-thimble path integral for solving the mean-field sign problem

2016 ◽  
Author(s):  
Yuya Tanizaki ◽  
Hiromichi Nishimura ◽  
Kouji Kashiwa
Keyword(s):  
Path Integral ◽  
Mean Field ◽  
Sign Problem ◽  
The Mean

The Non-effect of Polymer-Network Inhomogeneities in Microgel Volume Phase Transitions: Support for the Mean-Field Perspective

2014 ◽  
Vol 215 (11) ◽  
pp. 1116-1133 ◽  
Author(s):  
Axel Habicht ◽  
Willi Schmolke ◽  
Frank Lange ◽  
Kay Saalwächter ◽  
Sebastian Seiffert
Keyword(s):  
Phase Transitions ◽  
Polymer Network ◽  
Mean Field ◽  
Volume Phase ◽  
The Mean ◽  
Field Perspective

scholarly journals Structure of entangled polymer network from primitive chain network simulations

2010 ◽  
Vol 132 (13) ◽  
pp. 134902 ◽  
Author(s):  
Yuichi Masubuchi ◽  
Takashi Uneyama ◽  
Hiroshi Watanabe ◽  
Giovanni Ianniruberto ◽  
Francesco Greco ◽  
...  
Keyword(s):  
Polymer Network ◽  
Network Simulations ◽  
Entangled Polymer

FREE ENERGY AND THE STATIC POTENTIAL FOR OPEN SMOOTH STRINGS

1988 ◽  
Vol 03 (09) ◽  
pp. 2195-2206 ◽  
Author(s):  
K.S. VISWANATHAN ◽  
ZHOU XIAOAN
Keyword(s):  
Free Energy ◽  
Path Integral ◽  
Mean Curvature ◽  
Curvature Vector ◽  
Mean Curvature Vector ◽  
Static Potential ◽  
Negative Norm ◽  
Higher Derivative ◽  
The Mean

The methods of Polchinski, and Burgess and Morris are used and extended to evaluate Polyakov’s path integral for open, oriented smooth strings on a cylinder. The smooth string action possesses an (on-shell) invariance under normal variations in the direction of the mean curvature vector of the imbedded surface provided the surface is stationary. Fixing this gauge in the path integral allows one to eliminate all negative norm states arising from higher derivative terms. The free energy and the static potential of the smooth strings are computed. We find that the open smooth strings can be made tachyon-free and has the preferred coefficient −π/6 for the 1/R term in the static potential (for d=4) for large R.

Magnetoconductivity of Aluminum Computed by the Path-Integral Method

1973 ◽  
Vol 51 (16) ◽  
pp. 1770-1785 ◽  
Author(s):  
R. J. Douglas ◽  
W. R. Datars
Keyword(s):  
Field Dependence ◽  
Path Integral ◽  
Integral Method ◽  
Relaxation Times ◽  
Longitudinal Component ◽  
Zero Field ◽  
Temperature Dependent ◽  
The Mean ◽  
Carrier Velocity ◽  
Path Integral Method

The components of the electrical magnetoconductivity and magnetoresistivity tensors of aluminum were calculated by the path-integral method using a nearly-free-electron Fermi surface and a uniform relaxation time. Results are presented for longitudinal and transverse magnetoresistance, the longitudinal–transverse components, and the Hall term. The induced torque calculated from the computed magnetoresistivity components is in excellent agreement with measured anisotropy and field dependence of the induced torque. The torque anisotropy results primarily from the longitudinal magnetoresistance anisotropy which arises from variations with crystal orientation of the mean of the orbitally averaged longitudinal component of carrier velocity. The observed magnetic field dependence of the Hall coefficient is reproduced using a temperature-dependent ratio of the relaxation times for the electron and hole bands. The irreducible even-field Hall terms, which are calculated for field directions in the (112) plane, are discussed. The longitudinal–transverse components of magnetoresistivity can saturate at values as high as 0.16 of the zero-field resistivity, but the effects of the longitudinal–transverse magnetoconductivity on the magnetoresistance and Hall coefficients are small. Reported linear high-field magnetoresistance is discussed.

PATH-INTEGRAL APPROACH TO A POLYMER CHAIN IN RANDOM MEDIA WITH LONG-RANGE DISORDER CORRELATIONS

2005 ◽  
Vol 19 (29) ◽  
pp. 4381-4387
Author(s):  
CHERDSAK KUNSOMBAT ◽  
VIRULH SA-YAKANIT
Keyword(s):  
Long Range ◽  
Polymer Chain ◽  
Path Integral ◽  
Random Media ◽  
Integral Approach ◽  
Mean Square ◽  
Path Integral Approach ◽  
End Distance ◽  
The Mean ◽  
End To End

In this paper we consider the model of a flexible polymer chain embedded in a quenched random medium with long-range disorder correlations. Using the Feynman path integral approach we show that for the case of long-range quadratic correlations, we obtain an analytical result. The result is [Formula: see text], where 〈R2〉 is the mean square end-to-end distance of the polymer chain, ξ is the correlation length of disorder, Δ is an unknown parameter, b is the Kuhn step length, ρ is the density of random obstacles and N is the number of links. It is shown that for a polymer chain in a random media with long-range quadratic correlations, where ρ is not too high, the behavior of the polymer chain is like that of a free chain. This result agrees with the calculation using the replica method. However, in a medium where ρ is very high, the variation of the mean square end-to-end distance with disorder and its distance depending on ρ are found in our approach.

Controlling Toughness of Polymer-grafted Nanoparticle Composites for Impact Mitigation

Soft Matter ◽  
2022 ◽  
Author(s):  
Shawn H. Chen ◽  
Amanda J. Souna ◽  
Stephan Jeffrey Stranick ◽  
Mayank Jhalaria ◽  
Sanat Kumar ◽  
...  
Keyword(s):  
Unit Volume ◽  
Polymer Network ◽  
New Paradigm ◽  
Load Bearing ◽  
Topological Constraints ◽  
Impact Mitigation ◽  
Entangled Polymer ◽  
Grafted Nanoparticle ◽  
Nanoparticle Composites

Toughness in an entangled polymer network is typically controlled by the number of load-bearing topological constraints per unit volume. In this work, we demonstrate a new paradigm for controlling toughness...

Sign in / Sign up

Export Citation Format

Share Document